A variation of this technique, radial immunodiffusion (RID) computes concentration of antibody (or antigen) by measuring the diameter of a ring of precipitation formed from the interaction between the substance of interest, and gel-immobilized  antigen (or antibody). The diameter measurement permits the computation of the area inside the ring which is functionally related to concentration.

        Utilizing electrophoresis to first separate components of a mixture in a gel, then visualizing precipitation bands corresponding to the components through a process similar to double diffusion (with several specific antibodies) is the basis of immunoelectrophoresis. The reliable quantification of the results has been reviewed in Axelsen and Bock, 1972, with specific examples in Birkmeyer, et al., 1981. In Chen, et al., 1994, a simulation of the melting of DNA along with temperature gradient electrophoresis is used.

nephelometry

        In nephelometry, estimation of antibody or antigen concentrations is accomplished through the use of the light-scattering properties of complexes. It is a modification of the precipitin reaction in that the measurements of increased scattering due to complexes is done in the antibody excess zone. Repeated measurements are made as the antigen (or antibody) is titrated -- using a calibration curve to estimate the concentration of interest. Deverill and Reeves, 1980 reviews applications of the measurement of turbidity in this immunological setting. The basic mathematical problem is that the relationship between absorbance and antigen concentration is nonlinear (Foster and Ledue, 1986). An example can be found in Cambiaso et al., 1974.

immunofluorescence and fluorescent labeling of cells

        Antigens or antibody can be given fluorescent labels, with the objective generally being to localize or quantify the binding of antibody to specific sites in tissues or on cells. The assay is an immunofluorescence assay if labeled antibody is used and fluoroimmunoassay if antigen is labeled. In addition, cells are given fluorescent labels by antibody specific for distinguishing markers before sorting these cells in a fluorescence activated cell sorter (FACS). A similar process for the fluorescent microscope is also used to localize markers, their density, and distribution on cells of interest.

        To measure the concentration of antibody in serum to a given antigen, often in frozen sections or tissues, a fluorescein-conjugated anti-Ig antibody with the ability to bind all antibodies of interest is used in the immunofluorescence assay. After incubation of the serum with the tissue, gentle washing leaves antibody which binds to the tissue. Fluorescent-tagged anti-Ig is added, binding to all bound antibodies. The level of fluorescence observed is often proportional to the quantity of antibody which has bound to the tissue. This is the "indirect" procedure which is more sensitive that the "direct" procedure in which all antibody in the test sera is labeled. As a quantitative assay, there are difficulties with the indirect method as several labeled antibodies can bind to a single antibody of interest, and as a result, the amount of fluorescence in a sample depends on several parameters. This, and related problems are studied in Jobbágy and Jobbágy, 1972a; Jobbágy and Jobbágy, 1972b; and Coleman, et al., 1972. Quantitative aspects of the fluorescent labeling of cells for fluorescent microscopy can be in Dormer, et al., 1981; Pachmann and Killander, 1976; and Hesford, et al., 1987. Aspects of fluorescent labeling in flow cytometry is seen in the review Rolland, et al., 1985 and in Bardsley et al., 1992.